In OTL, Franklin Delano Roosevelt removed gold coins from circulation in 1933 (some people mistakenly call this "abandoning the gold standard" which is technically untrue). One of the apparent reasons was so the government could raise the official price of gold from $20.67/oz. to $35.00/oz.
However, it's a little-known fact that the U.S. raised the official price of gold once before, in 1834, from $19.29/oz. to $20.67/oz., without confiscating gold. The physical sizes of the coins were simply reduced. Of course, most people turned in their coins for reminting at the more favourable price: pre-1834 U.S. gold coins are quite rare for this reason.
It appears the reason the 1933 price increase was accompanied by confiscation was so the government would have the difference to spend on the New Deal. The 1834 increase was for a different reason: to reconcile the gold/silver ratio with that of the world markets to stop gold from leaving the country.
What if Roosevelt had the opinion that putting more nominal dollars in circulation was the key to ending the Depression, and the simplest way was to raise the price of gold to $35.00/oz., but not confiscate it. New gold coins would be issued at a smaller size, the new $10 and $20 would be slightly larger than the old $5 and $10.
Would the course of the Depression have been any different? Would public opinion of Roosevelt been any different? Any possible butterflies regarding OTL World War II?